www.ann-geophys.net/33/1271/2015/ doi:10.5194/angeo-33-1271-2015
© Author(s) 2015. CC Attribution 3.0 License.
The relationship between plasmapause, solar wind and geomagnetic
activity between 2007 and 2011
G. Verbanac1, V. Pierrard2,3, M. Bandi´c4, F. Darrouzet2, J.-L. Rauch5, and P. Décréau5 1Department of Geophysics, University of Zagreb, Zagreb, Croatia
2Belgian Institute for Space Aeronomy (Space Physics and STCE), 3 Av. Circulaire, 1180 Brussels, Belgium 3Université Catholique de Louvain, TECLIM, Earth and Life Institute, Place Louis Pasteur 3 bte L4.03.08, 1348 Louvain-La-Neuve, Belgium
4Preziosastr. 15a, 81927 München, Germany
5Laboratoire de Physique et Chimie de l’Environnement et de l’Espace (LPC2E), Orléans, France Correspondence to:G. Verbanac (giuli1.verbanac@gmail.com)
Received: 11 May 2015 – Revised: 23 July 2015 – Accepted: 4 September 2015 – Published: 16 October 2015
Abstract. Taking advantage of the Cluster satellite mis-sion and especially the observations made by the instrument WHISPER to deduce the electron number density along the orbit of the satellites, we studied the relationships between the plasmapause positions (LPP) and the followingLPP indi-cators: (a) solar wind coupling functionsBz(Zcomponent of the interplanetary magnetic field vector,B, in GSM system),
BV (related to the interplanetary electric field;Bis the mag-nitude of the interplanetary magnetic field vector, V is so-lar wind velocity), and d8mp/dt (which combines different physical processes responsible for the magnetospheric activ-ity) and (b) geomagnetic indices Dst, Ap and AE. The anal-ysis is performed separately for three magnetic local time (MLT) sectors (Sector1 – night sector (01:00–07:00 MLT); Sector2 – day sector (07:00–16:00 MLT); Sector3 – evening sector (16:00–01:00 MLT)) and for all MLTs taken together. All LPPindicators suggest the faster plasmapause response in the postmidnight sector. Delays in the plasmapause re-sponses (hereafter time lags) are approximately 2–27 h, al-ways increasing from Sector1 to Sector3. The obtained fits clearly resolve the MLT structures. The variability in the plasmapause is the largest for low values ofLPPindicators, especially in Sector2. At low activity levels,LPPexhibits the largest values on the dayside (in Sector2) and the smallest on the postmidnight side (Sector1). Displacements towards larger values on the evening side (Sector3) and towards lower values on the dayside (Sector2) are identified for enhanced magnetic activity. Our results contribute to constraining the
physical mechanisms involved in the plasmapause formation and to further study the still not well understood related is-sues.
Keywords. History of geophysics (solar–planetary rela-tionships) – interplanetary physics (interplanetary magnetic fields; instruments and techniques)
1 Introduction
The plasmasphere is the continuation of the ionosphere into the magnetosphere and represents the region of cold and rel-atively dense plasma in the inner magnetosphere (Lemaire and Gringauz, 1998; Darrouzet et al., 2009a). The base of the plasmasphere is defined as the transition from atomic oxygen to atomic hydrogen and occurs at altitudes between 500 and 2000 km depending on the geophysical conditions (Prölss, 2004a). The outer boundary of the plasmasphere, called the plasmapause, represents the cutoff in the plasma density, the location of which depends on the level of the geomagnetic disturbances. In the equatorial plane the plasmapause is typ-ically found near 5–7RE(e.g., Chappell et al., 1970a; Car-penter and Lemaire, 2004; Pedatella and Larson, 2010).
geomagnetic field. The corotation electric field is produced in the E region of the ionosphere and is conveyed into the plasmasphere along the magnetic field lines. During increas-ing magnetic activity, the stronger convection electric field pushes the plasmapause closer to the Earth (down to 2RE Goldstein et al., 2004), peeling off the outer layers of the plasmasphere. On the other hand, during decreasing activity the plasmapause moves outward, and a slow refilling process from the dayside F region ionosphere begins. These charac-teristics are in agreement with the observations of Cluster (e.g., Darrouzet and De Keyser, 2013) and IMAGE satellite data (e.g., Goldstein et al., 2004).
The LPPand its dependence on the geomagnetic activity have been studied both theoretically and empirically. The LPP has been directly related to the time variations in the convection electric field.
Two theoretical approaches have been used to describe the dynamics of the LPP: (i) the last closed streamline of the equatorial plasma related to the last closed equipotential of the electric field (Brice, 1967; Lemaire and Pierrard, 2008) and (ii) the interchange instability mechanism appearing in the postmidnight sector during geomagnetic storms and sub-storms (Pierrard and Lemaire, 2004; Lemaire and Pierrard, 2008).
EmpiricalLPP has been estimated by examining ground-based whistler observations, in situ satellite density measure-ments (e.g., ISEE, CRRES), field-aligned current signature observations (CHAMP) and geomagnetic indices (Chappell et al., 1970b; Horwitz et al., 1986; Carpenter and Anderson, 1992; Gallagher et al., 2000; Moldwin et al., 2002; O’Brien and Moldwin, 2003; Heilig and Lühr, 2013).
The often cited model of Carpenter and Anderson (1992) gives the LPP as a function of the maximum of the geo-magnetic Kp index observed in the previous 24 h. Moldwin et al. (2002) expressed the LPP as a function of the maxi-mum Kp index in the previous 12 h. O’Brien and Moldwin (2003) extended that investigation by using Kp, Dst and AE geomagnetic indices taking the hours relative to the plasma-pause crossing: 36 for Kp, 24 for Dst and 36 for AE. The new feature in their model is theLPPmagnetic local time (MLT) dependence.
They obtained a little difference in the quality of the plasmapause models for different indices and a lack of lo-cal time dependences in the Dst model. A new empirilo-cal model of theLPPbased on field-aligned currents measured by the CHAMP (CHAllenging Minisatellite Payload) satel-lite was introduced by Heilig and Lühr (2013). All these stud-ies found that the plasmapause is more earthward during ge-omagnetically active periods with the plasmapause bulge dis-placed toward dusk.
In the three-dimensional dynamic model of the plasma-sphere (Pierrard and Stegen, 2008) that has been recently coupled to the ionosphere (Pierrard and Voiculescu, 2011), the plasmapause depends on the MLT and on the Kp in-dex observed during the last 24 h. During substorm and
storm events, the geomagnetic activity increases and en-hances the convection electric field, mainly in the postmid-night MLT sector. This leads to an inward motion of the plasmapause closer to the Earth in this sector and then later in other MLT sectors due to the corotation of the plasma-pause with the Earth. Using a E5D convection electric field (McIlwain, 1986), the equatorialLPPis calculated in all MLT sectors and is provided on the European space weather por-tal (www.spaceweather.eu). Using the same mechanism but stronger convection electric fields, the plasmapause position is found to be closer to the Earth (Pierrard et al., 2008).
Larsen et al. (2007) correlated the average plasmapause radial positions observed by the EUV (Extreme Ultraviolet Imager) instrument on IMAGE with the solar wind parame-ters:Bz (Z component of the interplanetary magnetic field, IMF, vectorB in the geocentric solar magnetospheric sys-tem, GSM), the IMF clock angle, and the polar cap potential dropφ. TheLPPis found to be most tightly correlated with Bz. The time lags in the plasmapause response toBzand IMF clock angle were found to be 180 min, and 240 min with re-spect toφ.
In the present study, we investigate theLPP determined by the WHISPER (Waves of HIgh frequency and Sounder for Probing of Electron density by Relaxation) instrument (Décréau et al., 1997) on board Cluster as a function of vari-ousLPPindicators:
a. solar wind coupling functionsBz, BV related to the in-terplanetary electric field (B is the magnitude of the IMF vectorB,Vis solar wind velocity), and novel func-tion d8mp/dtintroduced by Newell et al. (2007), which combines different physical processes responsible for the magnetospheric activity and is explained in detail in Sect. 2;
b. geomagnetic indices Dst, Ap and AE.
We carry out our investigation by applying the cross-correlation analysis. The study is performed separately for three MLT sectors (Sector1 – night sector (01:00– 07:00 MLT); Sector2 – day sector (07:00–16:00 MLT); Sec-tor3 – evening sector (16:00–01:00 MLT)) and for all MLT taken together. Our approach is based on theLPPindicator values at the highest-correlation time lag, instead of the in-terval maxima as in previous studies listed above.
2 Data sets and method
Our study is based on the following data sets:
– 1-hour averages of geomagnetic indices Dst and AE; – 3-hour averages of geomagnetic index Ap;
– 1-hour averages of the solar wind parameters (velocity V, IMF magnitude B and componentsBx, By,Bz in GSM coordinate frame of the IMF vectorB);
– time–frequency electric field spectrograms during the plasmasphere crossing.
The planetary geomagnetic activity index, Ap, the storm-time disturbance index, Dst, and the auroral electrojet in-dex, AE, are downloaded from ftp://ftp.ngdc.noaa.gov/STP/ GEOMAGNETIC_DATA/INDICES/KP_AP and http://wdc. kugi.kyoto-u.ac.jp/dstae/index.html. For more detailed infor-mation about the indices, we refer to Prölss (2004b) and Ver-banac et al. (2010, 2011). Among the available geomagnetic indices, these three indices have been chosen for describing theLPPas a function of geomagnetic activity because their variations can be physically interpreted and related to the specific magnetospheric current system (e.g., the ring cur-rent and polar electrojet). In this context, the widely used Kp index is difficult to interpret. However, it is related to the Ap index, which is more convenient to use since it is based on a linear scale.
The solar wind data were obtained from the Solar Wind Electron Proton and Alpha Monitor (SWEPAM; McComas et al., 1998) and the magnetometer (MAG; Smith et al., 1998) on board the Advanced Composition Explorer (ACE; Stone et al., 1998). We used the merged hour-averaged level-2 ACE data given at http://www.srl.caltech.edu/ACE/ASC/level2/.
We note that different coupling functions between the so-lar wind and the magnetosphere have been investigated by many authors (e.g., Gonzalez et al., 1994, and references therein). Their relative importance has often been revised (e.g., Newell et al., 2007).
For the correlation study we analyzed the followingLPP indicators based on the solar wind basic and derived param-etersBz, BV and d8mp/dt(Newell et al., 2007), defined as d8mp/dt=V4/3BT2/3sin8/3(θc/2), (1) whereBT =
q
By2+Bz2is the projection of IMF vector in the Y–Zplane andθc=arctan(By/Bz)is the IMF clock angle in GSM.
These coupling functions have been chosen because their role in changing the state of the magnetosphere may be phys-ically interpreted. The conditions or processes that represent each of these functions are as follows. The energy transfer from the solar wind into the magnetosphere is most favorable when the IMF has a strong Bz component oriented south-ward. Then a reconnection with the Earth’s magnetic field
becomes possible, and consequently the strength of convec-tion increases, leading to the modificaconvec-tion of the plasmapause position. The BV quantity is directly related to the interplane-tary electric field and thus to the changes in the plasmapause shape and position. Studies by Verbanac et al. (2013) have shown that the magnetosphere responds in different man-ners to different solar drivers, e.g., coronal mass ejections and corotating interaction regions. They further show that the same BV range plays an equally important role for both types of magnetospheric drivers. Since in the present study we do not aim to make the distinction between the solar drivers of geomagnetic disturbances, we chose the BV quantity as the representative coupling function. Verbanac et al. (2013) also found that BV is strongly correlated with geomagnetic in-dices Ap, AE and Dst, so we expected this quantity to be a good measure for the response of the plasmapause as well.
The quantity d8mp/dt combines different physical pro-cesses responsible for the magnetospheric activity, such as the rate at which IMF field lines are convected toward the magnetopause, the fraction of field lines impacting the mag-netosphere that merge, the amount of the opened flux, the length of the merging line. Newell et al. (2007) showed that among 20 employed coupling functions, d8mp/dtrepresents the interaction between the solar wind and magnetosphere best for a wide variety of geomagnetic activity, even better than BsV (Bs is zero forBz>0) which is one of the most widely used coupling function, and thus is used in the present study.
The analyzedLPPare determined from data provided by the WHISPER instrument on board the Cluster satellites. The Cluster mission consists of four identical spacecraft (C1, C2, C3, and C4) launched in 2000 on similar elliptical polar or-bits with a time period of 57 h. The initial perigee was about 4REand the apogee at 19.6RE(Escoubet et al., 2001). Each satellite crosses the inner magnetosphere from the Southern to the Northern Hemisphere around the perigee. Due to the annual precession of the orbit, all MLTs are covered over the course of a year. Each spacecraft carries 11 instruments. The WHISPER data allow determining the electron density inside and outside the plasmasphere (Décréau et al., 2001; Darrouzet et al., 2009b; Lointier et al., 2013). The frequency spectra obtained during the passive and active (sounding) op-eration modes of the instrument carry out a direct or indi-rect determination of the electron plasma frequencyFP. The electron densityNe is deduced fromFP by the relationNe (cm−3) =F2
P(kHz)/81. The instrument can estimate electron densities up to 80 cm−3due to the instrument frequency
up-per limit at 80 kHz, with a temporal resolution of 2 s on aver-age. The uncertainty on the plasma frequency measurements is 163 Hz, which gives a relative error on electron density of the order of 0.5–5 % at densities higher than 20 cm−3 (Dar-rouzet et al., 2013).
plasma-Fp
Figure 1.Time–frequency electric field spectrograms measured by the instrument WHISPER on board the four Cluster spacecraft on 23 Oc-tober 2011, between 17:00 and 23:00 UT. The plasmapause position corresponds to the sharp increase in the electron plasma frequencyFP
(visible as the clear blue line, indicated by the red arrows for C3), directly related to the electron density. The orbital parameters shown below the figure correspond to C4.
pause). During the investigated time period (2007–2011), the satellites orbit with the perigee located inside the plasmas-phere, as close as 2RE, allowed us to determine the electron density inside and outside the plasmasphere from WHISPER (Darrouzet et al., 2013). We have used two different and com-plementary data sets of plasmapause positions determined from WHISPER data, during two different time periods and two different orbitographies. The first data set (April 2007 to March 2009) was determined by Darrouzet et al. (2013). During this time period, we have only used the LPP deter-mined from C3 because all three instruments needed in this first study were functioning well only on board this satellite. We have considered only the inbound crossings because the inbound and outbound ones were separated by only a few UT hours and a limited MLT difference (see, for instance, Figs. 1 and 3 of Lointier et al., 2013). We have further supplemented
of the density ramp is considered the position of the plasma-pause. Note that the upper limit of the instrument is indeed low and induces limitations in our plasmapause determina-tion technique. However, we have excluded from our statis-tical study the events with small-density gradients and small maximum electron density values (see the typical strong den-sity gradient of our events on Fig. 1). Then we consider that the events selected here give an innermost plasmapause po-sition, not far from the plasmapause position that would be defined as the middle of the plasmasphere boundary layer. Note that in this way, we have the same plasmapause posi-tion definiposi-tion as in the study of Li et al. (2006). The presence of plasmaspheric plumes (Darrouzet et al., 2006, 2008) were further taken into account. We simply looked for the plasma-pause and checked the presence of a plume. If there was one, we took care to not use the inner boundary of the plume as the plasmapause. In Fig. 1 we show an example of time– frequency electric field spectrograms measured by WHIS-PER on board the four Cluster satellites (C1, C2, C3, and C4) on 23 October 2011, between 17:00 and 23:00 UT. The plasmapause corresponds to the sharp increase in the elec-tron plasma frequency, as seen for instance around 18:00 UT during the C1, C3 and C4 inbound plasmapause crossing and around 18:30 UT for C2 (see, respectively, the panels 1, 3, 4 and 2 of Fig. 1).
The relationships between the LPP and both the solar-wind- and Earth-based LPP indicators are then investi-gated for three different MLT sectors (Sector1 – night sector (01:00–07:00 MLT); Sector2 – day sector (07:00– 16:00 MLT); Sector3 – evening sector (16:00–01:00 MLT)) and for all MLT taken together (details and results of the analyses are presented in Sect. 4). Sector1, Sector2 and Sec-tor3 contain 67, 64 and 180 plasmapause crossings, respec-tively. Such MLT intervals were selected to ensure, as much as possible, adequate statistics in each time bin. The cross-correlation analysis is applied and the delay times of the plasmapause toLPPindicators are obtained. The time series to correlate are created as follows.
One series contains the determined LPP which refers to the specific times (e.g., 7 April 2007, 19:49:48 UT). The sec-ond time series (of the same length asLPP) consists of given LPPindicator values taken at a fixed time lag1twith respect toLPP. A correlation coefficient is computed between these two time series and then the procedure is repeated for time lags ranging between 0 and 30 h, with a step of 1 h (data res-olution). The hour (UT) at which the plasmapause crossing begins (e.g., 19:00:00 UT for the plasmapause crossing on 7 April 2007 at 19:49:48 UT) is taken as the time for the first value of the second time series.
A given X–Y correlation corresponds to the linear form Y (t )=aX(t∗)+b, whereX(t∗) represents the value ofX that occurred1t hours before the true value ofY (t ). Thus t∗is the “retarded time” (t∗=t−1t). Negative lag between
two quantities, e.g., BV andLPP, hereinafter denoted as the BV–LPPcorrelation, means that BV is delayed with respect
0 5 10 15 20 25 30
−0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1
Time lag (hours)
Cross−correlation coefficient (Sector 1)
0 5 10 15 20 25 30
−0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1
Time lag (hours)
Cross−correlation coefficient (Sector 1)
Figure 2.Cross-correlation function describing the BV–LPP(top)
and AE–LPP (bottom) relationships for MLT Sector1 (01:00–
07:00 MLT). The red cross indicates the highest-correlation-coefficient time lag.
Table 1.Total number of plasmapause positions and the minimum
and maximum plasmapause position observed during different pe-riods of solar activity: low phase (2007–2009) and increasing phase (2010–2011) of the solar cycle 23.
Period Total number Lmin(RE) Lmax(RE)
of positions
2007–2009 80 3.7 8.8 2010–2011 231 2.9 7.6 All years 311 2.9 8.8
toLPP. Such lags are not considered since they are not phys-ical. Note that the zero time lag actually means any delay between 0 and 1 h. Further note that using an upstream mon-itor ACE, the obtained time lags related to the solar-wind-basedLPP indicators contain the response of the magneto-sphere plus the propagation time (the time that the solar wind propagates between ACE position and the nose of the mag-netosphere, which is∼1 h on average).
Table 2.Characteristics of the analyzed data set. The minimum or the maximum is taken over the interval of 30 h prior to the plasmapause crossing. Two values given forBzrefer to southward and northwardBzorientation (Bz<0 andBz>0).
BV V B Bz Dst Ap AE
(mV m−1) (km s−1) (nT) (nT) (nT) (nT) (nT)
allLPPvalues 11.1 680 24.5 −16.5,21.6 −132 154 1287
LPP=2.9RE 4.7 650 8 −3.8,3 −40 40 950
LPP=8.8RE 1.5 310 3.5 −2,2.3 −10 4 130
Table 3. The cross-correlation coefficientsR and the corresponding time lags 1t (in hours) of the relationship betweenLPP andLPP
indicators (Bz, BV, d8mp/dt, Dst, Ap, AE) for the highest-correlation time lags. NegativeRdenotes anticorrelation betweenLPPindicators andLPP. The last four columns are the rms errors (σ) of the bestLPPfits. Subscripts “i” and “all” refer to the MLT Sectors1–3 (Sec1:
01:00–07:00 MLT; Sec2: 07:00–16:00 MLT; Sec3: 16:00–01:00 MLT) and to all MLT sectors, respectively.
R1 1t R2 1t R3 1t Rall 1t σ1 σ2 σ3 σall
Bz–Lpp 0.54 2 0.39 14 0.36 23 0.31 23 0.74 1.18 0.85 0.96
BV–Lpp −0.71 11 −0.66 15 −0.57 27 −0.53 27 0.62 0.96 0.73 0.86
d8mp/dt−Lpp −0.65 2 −0.63 14 −0.55 20 −0.46 23 0.68 0.99 0.72 0.88 Dst–Lpp 0.71 0 0.73 7 0.64 14 0.57 7 0.62 0.87 0.70 0.83
Ap–Lpp −0.69 5 −0.64 11 −0.59 21 −0.53 10 0.63 0.98 0.74 0.85 AE–Lpp −0.74 5 −0.6 12 −0.6 20 −0.53 20 0.59 1.03 0.72 0.86
The 24 h time range was first examined and then an addi-tional, significant peak in the cross-correlation functions of all quantities around1t=27 h was identified. Accordingly
the time interval has been enlarged. The highest correlation coefficient in each of the MLT sectors and also when all MLT are binned together is always found at a time lag of less than 30 h, and thus we took the length of 30 h as optimal. This investigation of the most appropriate time interval prior to the plasmapause crossing indicates that it likely takes sev-eral hours for any change in theLPPto propagate around the Earth for MLT sectors other than the postmidnight one (see also Lemaire and Pierrard, 2008). As an example in Fig. 2, we present the cross-correlation function between BV and LPP and AE and LPP in MLT Sector1. An increase in in-dicator value (here BV or AE) will cause shrinking of the plasmapause (a decrease inLPP), which means that the cor-relation is negative. The highest-corcor-relation-coefficient time lag (1t=11 and1t=5 h) is indicated in the figures with
red cross. Note the appearance of the secondary peak at 1t=27 h in the bottom panel of Fig. 2.
3 Characteristics of the analyzed samples
In addition to showing the minimum and maximum plasma-pause extension, Table 1 contains the number of determined LPPfor the two solar activity periods: the low (2007–2009) and the increasing phase (2010–2011).
To determine theLPP, we processed the data collected by Cluster. Sometimes there are no data because the instrument is off, the satellite is off or because there are eclipses.
Some-times, the plasmapause is crossed at too high density so that its position cannot be clearly identified. This results in the un-equal data distribution through considered years. Note that most of the determined LPP come from measurements ob-tained in 2011. TheLPPranges between 2.9 and 8.8RE. The mean LPP obtained by averaging all 311 determined LPP values amounts to 5.6RE. Except for 2011, the considered time span includes declining, minimum and early increasing phases of the solar cycle. During this period (2007–2010) the geomagnetic activity was mostly low, and consequently the plasmapause was located quite far from the Earth (on average at 7.9RE). As the solar activity starts to increase in 2011, we observed that the plasmapause shrinks to as low as 2.9RE.
To give an overview of the characteristics of the analyzed samples, we present in Table 2 the maximal values of 1 AU solar wind parameters (basic and derived) studied and ge-omagnetic indices related to the LPP closest to the Earth (2.9RE),LPPfurthest from the Earth (8.8RE) and to all con-sideredLPP values. Maxima are taken over the interval of 30 h prior to the plasmapause crossing. For all parameters maxima are considerably different for low and high solar ac-tivity periods. The two values given forBzrefer to southward and northwardBzorientation (Bz<0 andBz>0).
The lowest plasmapause that occurred in 2011 is not as-sociated with the largest solar wind parameters and also not with the largest geomagnetic indices found within the used data sets. Note that according to the highest amplitude Dst (Dst= −40 nT), geomagnetic activity was weak (Sugiura
T able 4. Linear least-squares fits ( y = a x + b ) for the relationships between LPP and LPP indicators ( Bz ,BV ,d 8mp / d t ,Dst, Ap, AE) for the highest-correlation time lags. S ubscripts “ i ” and “all” refer to the ML T Sectors1–3 and to all ML T sectors, respecti vely . a1 b1 a2 b2 a3 b3 aall ball Bz (2 . 15 ± 0 . 42 ) × 10 − 1 4 . 83 ± 0 . 09 (3 . 04 ± 0 . 92 ) × 10 − 1 5 . 51 ± 0 . 15 (1 . 51 ± 0 . 30 ) × 10 − 1 5 . 21 ± 0 . 07 (1 . 45 ± 0 . 26 ) × 10 − 1 5 . 18 ± 0 . 06 BV ( − 4 . 77 ± 0 . 63 ) × 10 − 1 5 . 78 ± 0 . 16 ( − 9 . 43 ± 1 . 36 ) × 10 − 1 7 . 24 ± 0 . 29 ( − 3 . 27 ± 0 . 36 ) × 10 − 1 5 . 96 ± 0 . 09 ( − 3 . 73 ± 0 . 35 ) × 10 − 1 5 . 96 ± 0 . 09 d 8mp / d t ( − 1 . 83 ± 0 . 27 ) × 10 − 4 5 . 32 ± 0 . 11 ( − 3 . 36 ± 0 . 53 ) × 10 − 4 6 . 47 ± 0 . 20 ( − 1 . 43 ± 0 . 17 ) × 10 − 4 5 . 61 ± 0 . 07 ( − 1 . 63 ± 0 . 18 ) × 10 − 4 5 . 59 ± 0 . 07 Dst (4 . 06 ± 0 . 51 ) × 10 − 2 5 . 12 ± 0 . 09 (8 . 55 ± 1 . 02 ) × 10 − 2 6 . 04 ± 0 . 13 (3 . 59 ± 0 . 32 ) × 10 − 2 5 . 61 ± 0 . 06 (4 . 40 ± 0 . 36 ) × 10 − 2 5 . 49 ± 0 . 05 Ap ( − 4 . 75 ± 0 . 62 ) × 10 − 2 5 . 19 ± 0 . 09 ( − 16 . 96 ± 2 . 56 ) × 10 − 2 6 . 31 ± 0 . 18 ( − 3 . 95 ± 0 . 41 ) × 10 − 2 5 . 62 ± 0 . 06 ( − 8 . 12 ± 0 . 72 ) × 10 − 2 5 . 66 ± 0 . 06 AE ( − 4 . 95 ± 0 . 56 ) × 10 − 3 5 . 38 ± 0 . 09 ( − 7 . 75 ± 1 . 33 ) × 10 − 3 6 . 21 ± 0 . 18 ( − 3 . 78 ± 0 . 37 ) × 10 − 3 5 . 72 ± 0 . 07 ( − 3 . 73 ± 0 . 34 ) × 10 − 3 5 . 63 ± 0 . 06
than the highest AE associated with the high-speed solar wind streams driving geomagnetic activity during solar cy-cle 23 as reported by Verbanac et al. (2013). It may indicate that in this case, the auroral electrojet played a more impor-tant role than the ring current in the formation of the plasma-pause. The largestLPP, which occurred in 2008, is preceded by much lower maximal values of both solar wind parame-ters and geomagnetic indices.
The maximal values of all LPP indicators are found for LPP=3.9RE and thus not for the lowest LPP within our sample. This confirms that the individual peak values of the plasmapause indicators may not be the most appropriate measure to characterize the plasmapause position.
4 Results
In the following we relate theLPP indicators to the deter-mined LPP by applying the cross-correlation analysis. We follow the method explained in Sect. 2. Most of the analyzed data distributions indicate that two (or even three, e.g., for AE) linear least-square relationships should be adopted, one for lower and the other for higher values of theLPP indi-cators. Since the period studied includes mostly periods of quiet solar activity, our data sets contain only few points at higherLPPindicator values which is certainly not enough to perform a reliable regression. Thus, the linear relationships are obtained by taking allLPPvalues within each of the three sectors and also when all MLT are binned together.
sec-0 2 4 6 8 10 0
2 4 6 8
L pp
[Re]
Sector1 (01−07 MLT) Time−lag = 11 h
0 2 4 6 8 10
0 2 4 6 8
L pp
[Re]
Sector2 (07−16 MLT) Time−lag = 15 h
0 2 4 6 8 10
0 2 4 6 8
L pp
[Re]
Sector3 (16−01 MLT) Time−lag =27 h
0 2 4 6 8 10
0 2 4 6 8
BV [mV/m] L pp
[Re]
All MLTs Time−lag = 27 h
Figure 3.TheLpp(RE) as a function of BV (mV m−1) for three
dif-ferent MLT Sectors (Sector1 (01:00–07:00 MLT); Sector2 (07:00– 16:00 MLT); Sector3 (16:00–01:00 MLT)) and for all MLTs binned together (from top to bottom). Red lines represent the linear fits for the highest-correlation time lag. Dashed lines represent the residual standard deviation.
0 200 400 600 800 1000 0
2 4 6 8
Lpp
[Re]
Sector1 (01−07 MLT) Time−lag = 5 h
0 200 400 600 800 1000 0
2 4 6 8
Lpp
[Re]
Sector2 (07−16 MLT) Time−lag = 12 h
0 200 400 600 800 1000 0
2 4 6 8
Lpp
[Re]
Sector3 (16−01 MLT) Time−lag = 20 h
0 200 400 600 800 1000 0
2 4 6 8
AE [nT]
L pp
[Re]
All MLTs Time−lag = 20 h
Figure 4.TheLpp(RE) as a function of AE (nT) for three different
tor. Similar1t are obtained for Ap and AE in all three sec-tors. Notably shorter1t are obtained for Dst (4–7 h shorter depending on the sector). It is interesting to note that for al-most all LPP indicators, we found a second peak at a time lag of around 27 h (see Fig. 2, bottom). This additional peak found at larger1tprobably causes the large1tvalues when all MLT are considered together. This should be investigated in a further study. The RMSEs are approximately 0.6–1.2RE in all sectors. For all indicators the RMSEs are the largest in Sector2. For solar wind parameters, the largest and the low-est RMSEs are found forBzand BV, respectively, regardless of the sector. A large RMSE forBz–LPPmost likely reflects the fact that a northward-orientedBzalso plays an important part in eroding the plasmapause, at least at lowerBzvalues. For instance, LPParound 3.7RE is observed atBz oriented northward. Note that these values are very similar to the low-estLPPvalues found for southwardBz. Concerning geomag-netic indices, the lowest RMSE is obtained for AE in Sector1 and for Dst in both Sector2 and Sector3 and all MLTs.
Linear least-squares fit coefficients for the highest-correlation time lag used to obtain the relationships between the LPPand consideredLPPindicators are presented in Ta-ble 4. For all LPP dependencies the slopes are the steepest in Sector2. The ratio between the slope in Sector2 and that in Sector1 or Sector3 is ∼4 for Ap–LPP, while it is ∼2
for the other LPP indicators. However, note that the slopes in Sector3 are somewhat lower than the slopes in Sector1. Thus, the same change in the specific LPP indicator will likely cause the largest movement ofLPPin Sector2 and the smallest in Sector3. According to parameter bof the linear least-squares fits, for all investigatedLPPdependences, the smallest plasmapause extension is allowed in the night sector (Sector1) and its largest extension in the day sector (Sector2) due to the plume formation.
We show the BV–LPP, AE–LPPand Dst–LPPscatterplots for the highest-correlation time lag in Figs. 3a–d, 4a–d and 5a–d, respectively. The fitted linear relations (solid lines) clearly show a trend of decreasingLPP with increasing BV and AE and increasing LPP with decreasing Dst. However, all displayed data distributions show that LPP only shrinks to a particular value as theLPPindicator increases and then appears to saturate. Namely, there is noLPPbelow∼3, 3.8,
3.3 and 3REin Sectors1–3 and all MLT, respectively. Since the majority of ourLPPvalues are placed at lower values of the analyzed LPP indicators, this must be taken only as an indication of the general plasmapause behavior.
The most probableLPPvalues in each of the three sectors and for all MLT are determined using the calculated linear fits for all of the LPPindicators. Table 5 contains the fitted LPP values for low and high activity. The indicator values at high activity are those at whichLPPcomes closest to the Earth. This happens in Sector2 for allLPPdependencies, and we associateLPP∼2.5REin Sector2 with high activity.
Note that these indicator values for high activity, which cause significant shrinking of the plasmapause, are
associ-−60 −40 −20 0 20 40
0 2 4 6 8
L pp
[Re]
Sector1 (01−07 MLT) Time−lag = 0
−60 −40 −20 0 20 40
0 2 4 6 8
L pp
[Re]
Sector2 (07−16 MLT) Time−lag = 7 h
−60 −40 −20 0 20 40
0 2 4 6 8
L pp
[Re]
Sector3 (16−01 MLT) Time−lag = 14 h
−60 −40 −20 0 20 40
0 2 4 6 8
Dst [nT] L pp
[Re]
All MLTs Time−lag = 7 h
Figure 5.TheLpp(RE) as a function of Dst (nT) for three different
Table 5.TheLPPobtained from the linear least-square fits listed in the Table 4 for low and high activity. The indicator values at high activity are those at whichLPPamounts to∼2.5REin Sector2. See text for details.
Bz(nT) BV (mV m−1) d8mp/dt(km s−1)4/3(nT)2/3 Dst (nT) Ap (nT) AE (nT)
−0.2 −10 1 5 0.5×104 1.2×104 −10 −40 5 22 30 475
Sect1 4.78 2.68 5.30 3.40 4.41 3.13 4.71 3.50 4.95 4.15 5.24 3.04 Sect2 5.45 2.47 6.30 2.52 4.80 2.45 5.19 2.62 5.47 2.58 5.98 2.53 Sect3 5.17 3.70 5.63 4.32 4.89 3.90 5.26 4.18 5.42 4.75 5.61 3.93 SeAll 5.15 3.73 5.59 4.10 4.77 3.64 5.05 3.73 5.25 3.87 5.52 3.86
ated with the stronger values ofLPPindicators although they are of moderate intensity, as seen in Table 5 (e.g., Dst= −40 nT). The reason is that our analysis is based on theLPP indicator value at the highest-correlation time lag instead of the interval maxima, as noted before.
Taking into account the RMSE given in Table 3, informa-tion aboutLPPreported in Table 5 shows that at low activity, the plasmapause is located closest to the Earth in Sector1 and furthest away from it in Sector2. At higher activity the clos-est plasmapause is found in Sector2 and the furthclos-est away in Sector3. These results reveal the MLT asymmetries at both low and higher activity levels. During low activity, day–night asymmetry is more prominent (with the bulge on the day-side). As activity increases, the bulge is displaced toward the evening, and day–evening asymmetry becomes more promi-nent. Interestingly, all the LPP indicators used provide us with the same conclusion.
5 Conclusions
The cross-correlation analysis was applied to study the plasmapause positionLPP, determined using the WHISPER instrument on board the Cluster satellites, as a function of various solar wind and Earth-basedLPPindicators. The max-imum (in an absolute sense) value of theLPPindicators that precedes the plasmapause crossing is generally higher for smallerLPPthan for largerLPP. However, our analyses show that the value at the highest-correlation time lag is more ap-propriate for describing the plasmapause responses to any disturbances rather than the maximum values in the prevail-ing interval before theLPP, as commonly used in other stud-ies (e.g., Moldwin et al., 2002; O’Brien and Moldwin, 2003, and references therein). Thus, the obtained results (fit pa-rameters) cannot be directly compared, but general findings confirm those of previous research (Carpenter and Anderson, 1992; Moldwin et al., 2002; O’Brien and Moldwin, 2003; Heilig and Lühr, 2013). All studies show that the plasma-pause is closer to Earth during geomagnetically active peri-ods, with the plasmapause bulge displaced toward dusk.
Delay times of the LPP in relation to the arrival of LPP indicators were obtained. The values range from 0 to 27 h, depending on the MLT sectors and on the LPP indicators.
The analysis is performed for three different MLT sectors (Sector1 – night (01:00–07:00 MLT); Sector2 – day (07:00– 16:00 MLT); Sector3 – evening (16:00–01:00 MLT)) and for all MLT taken together. Based on the correlation coeffi-cients and RMSE, we conclude that allLPPindicators stud-ied are capable of describing the observed plasmapause posi-tion well. Among solar wind coupling funcposi-tions, BV is found to be a slightly superiorLPPindicator in all sectors and for all MLT binned together. As regards geomagnetic indicators, AE is found to be the best one in Sector1 and Dst is the best in Sector2, Sector3, as well as for all MLT. O’Brien and Mold-win (2003) also found that AE is particularly effective in the night and dawn sectors. However, no MLT dependence is vis-ible in their Dst model.
Among all indicators,Bz provides the least reliableLPP. Generally, the correlations are the highest in Sector1 and de-crease through Sector2 to Sector3. OurBz–LPPcorrelation for all MLTs is somewhat lower than the one obtained by Larsen et al. (2007) and the time lag is very different. The discrepancy may result from different methodology and dif-ferent plasmapause observations used in both studies.
The obtained time lags increase from Sector1 to Sector3, for allLPP indicators. The time lag for BV–LPP is excep-tional in Sector1 and amounts to 11 h. Similar delays are ob-tained for Ap and AE in all three sectors. Notably shorter time delays (4–7 h shorter depending on the sector) are ob-tained for Dst, suggesting that the ring current may play an important role in quickly peeling off the plasmapause via non-convection processes.
pro-posed by Lemaire and Pierrard (2008). Our analysis further indicates that this instability propagates with a velocity that may slightly differ from the corotation velocity.
The scatter around the fit of the plasmapause is larger for lowest values of LPPindicators as noted also by Moldwin et al. (2002). This is the most prominent in Sector2. Ac-cording to our findings, LPP exhibits the largest values on the dayside (somewhere between 07:00 and 16:00 MLT) and smallest values in the postmidnight sector during low activ-ity levels. This is in agreement with Gringauz and Bezrukikh (1976). By contrast, Moldwin et al. (2002) noted a slight asymmetry in the noon–midnight direction, with anLPPpeak in the night sector. During more active periods, we observed that LPP peaks in the evening sector (between 16:00 and 01:00 MLT) and the smallest plasmapause expansions are found on the dayside (between 07:00 and 16:00 MLT). This is in agreement with results presented by O’Brien and Mold-win (2003) and Heilig and Lühr (2013), while this asymme-try was not found in any other studies (e.g., Gringauz and Bezrukikh, 1976; Carpenter and Anderson, 1992; Moldwin et al., 2002). Further, at enhanced magnetic activity, we ob-served a tendency forLPPto saturate as there is noLPP be-low a certain value (depending on the MLT sector). However, at highLPPindicator values, we do not have sufficient data points to make a general conclusion.
We plan to continue this study by enlarging ourLPPdata set, possibly during a period of higher solar activity. This will allow us to verify the obtained results and to more re-liably constrain the lower limit ofLPPfor various MLT sec-tors. Further, the possibility to perform the analyses look-ing at narrow MLT sectors will enable us to more precisely identify both the MLT in which the plasmapause is formed and the displacement of the bulge during the active mag-netic period. With the extension of our study, we hope to get a better insight into the physical mechanisms responsi-ble for the plasmapause formation. This is very important since the plasmapause plays a crucial role in the propagation of the mass and energy distribution within the inner magne-tosphere.
Acknowledgements. The results presented in this paper are based
on data from Cluster and ACE satellites and from the Kyoto World Data Center for geomagnetism. We thank all the staff involved for providing high-quality data. The presented work was initiated dur-ing G. Verbanac’s visit to the Belgian Institute for Space Aeron-omy, which was supported by the European Union Seventh Frame-work Programme (FP7/2007-2013) – COMESEP. G. Verbanac is especially thankful to N. Crosby (Project Coordinator and Team Leader of the COMESEP project) and B. Vrsnak (Croatian COME-SEP Team Leader) and to J. De Keyser. V. Pierrard thanks the STCE (Solar-Terrestrial Centre of Excellence) and the Belgian Federal Science Policy (Belspo) regarding the Interuniversity At-traction Pole program, project P7/08 CHARM. V. Pierrard and F. Darrouzet thank Belspo for the Cluster Prodex project (contract 13127/98/NL/VJ). All authors thank ESA for the Cluster mission.
We gratefully acknowledge constructive suggestions from the two reviewers.
The topical editor G. Balasis thanks B. Heilig and M. Vellante for help in evaluating this paper.
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